Six decks of $n$ cards, numbered from $1$ to $n$, are given. Melanie arranges each of the decks in some order, such that for any distinct numbers $x$, $y$, and $z$ in $\{1, 2, . . . , n\}$, there is exactly one deck where card $x$ is above card $y$ and card $y$ is above card $z$. Show that there is some $n$ for which Melanie cannot arrange these six decks of cards with this property.